There are two tangent lines to the parabola y=x^2 that pass through the point (0,-9). These tangent lines to the parabola pass through which two points respectively?

Answer 1

Hi Connor T., Draw a sketch of the parabola and the point (0, -9) which will be below the parabola. Now draw the tangent lines - one touches the parabola on the right, and the other touches the parabola on the left.

These lines both have a slope of 2x ( the derivative of x ^2). A point on the curve can be written as (x, x^2).

See if you can use the two-point slope formula from algebra class with (0, -9) and (x, x^2) to work out the answer. Tom S.